
as \((a_1,a_2)\rightarrow (0,0)\) . It follows that, up to a subsequence, \(\lbrace (u^-_{a_1},v^-_{a_2})\rbrace \)  is a minimizing sequence of the minimizing problem (REF ). From Lemma REF , \((u^-_{a_1},v^-_{a_2})\)  is radially symmetric. By [1]} or [2]}, up to a subsequence, there exists \(\sigma _1:=\sigma _1(a_1,a_2)\)  such that for some \(\varepsilon _0>0\) ,
\(u_1(x)=\sigma _1 u^-_{a_1}(\sigma _1 x)\rightarrow \sqrt{k_1}U_{\varepsilon _0}\ \ \text{and} \ \ v_1(x)=\sigma _1 v^-_{a_2}(\sigma _1 x)\rightarrow \sqrt{k_2}U_{\varepsilon _0}\) 
